The latest figures compare with 32,119 who made the journey by the same date in 2024 and 26,699 in 2023.
Mahmood is set to announce a major shake-up of the immigration and asylum system later this month.
She wants to reduce incentives for people seeking to enter the UK, while making it easier to remove those found to have no right to stay.
In September, the Home Office suspended new applications under the Refugee Family Reunion scheme, pending the drafting of new rules.
The tighter Danish rules on family reunions and restricting some refugees to a temporary stay are understood to be among the policies being looked at.
The home secretary is said to be impressed that Denmark has driven down its number of successful asylum claims to a 40-year low – with the exception of 2020, amid pandemic travel restrictions.
Mahmood pledged at the Labour Party conference in September to “do whatever it takes” to regain control of Britain’s borders.
But some in her party are against going down the Danish route, with one left-wing Labour MP saying it was too “hardcore” and contained echoes of the far right.
Additional reporting by PA.